List of dimensionless quantities

This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers, dimensionless ratios, or dimensionless physical constants; these topics are discussed in the article.

Biology and medicine

Name	Standard symbol	Definition	Field of application
Basic reproduction number	$R_{0}$	number of infections caused on average by an infectious individual over entire infectious period	epidemiology
Body fat percentage		total mass of fat divided by total body mass, multiplied by 100	biology
Kt/V	Kt/V		medicine (hemodialysis and peritoneal dialysis treatment; dimensionless time)
Waist–hip ratio		waist circumference divided by hip circumference	biology
Waist-to-chest ratio		waist circumference divided by chest circumference	biology
Waist-to-height ratio		waist circumference divided by height	biology

Chemistry

Name	Standard symbol	Definition	Field of application
Activity coefficient	$\gamma$	$\gamma ={\frac {a}{x}}$	chemistry (Proportion of "active" molecules or atoms)
Arrhenius number	$\alpha$	$\alpha ={\frac {E_{a}}{RT}}$	chemistry (ratio of activation energy to thermal energy)
Atomic weight	M		chemistry (mass of one atom divided by the atomic mass constant, 1 Da)
Bodenstein number	Bo or Bd	$\mathrm {Bo} =vL/{\mathcal {D}}=\mathrm {Re} \,\mathrm {Sc}$	chemistry (residence-time distribution; similar to the axial mass transfer Peclet number)
Damkohler number	Da	$\mathrm {Da} =k\tau$	chemistry (reaction time scales vs. residence time)
Hatta number	Ha	$\mathrm {Ha} ={\frac {N_{\mathrm {A} 0}}{N_{\mathrm {A} 0}^{\mathrm {phys} }}}$	chemical engineering (adsorption enhancement due to chemical reaction)
Jakob number	Ja	$\mathrm {Ja} ={\frac {c_{p}(T_{\mathrm {s} }-T_{\mathrm {sat} })}{\Delta H_{\mathrm {f} }}}$	chemistry (ratio of sensible to latent energy absorbed during liquid-vapor phase change)
pH	$\mathrm {pH}$	$\mathrm {pH} =-\log _{10}(a_{{\textrm {H}}^{+}})$	chemistry (the measure of the acidity or basicity of an aqueous solution)
van 't Hoff factor	i	$i=1+\alpha (n-1)$	quantitative analysis (Kf and Kb)
Wagner number	Wa	$\mathrm {Wa} ={\frac {\kappa }{l}}{\frac {\mathrm {d} \eta }{\mathrm {d} i}}$	electrochemistry (ratio of kinetic polarization resistance to solution ohmic resistance in an electrochemical cell)
Weaver flame speed number	Wea	$\mathrm {Wea} ={\frac {w}{w_{\mathrm {H} }}}100$	combustion (laminar burning velocity relative to hydrogen gas)

Physics

Physical constants

Main article: Dimensionless physical constant § Examples

Fluids and heat transfer

Main article: Dimensionless numbers in fluid mechanics

For a more comprehensive list, see List of dimensionless numbers in fluid mechanics.

Name	Standard symbol	Definition	Field of application
Archimedes number	Ar	$\mathrm {Ar} ={\frac {gL^{3}\rho _{\ell }(\rho -\rho _{\ell })}{\mu ^{2}}}$	fluid mechanics (motion of fluids due to density differences)
Asakuma number	As	$\mathrm {As} ={\frac {W}{\alpha \rho d_{p}H}}$	heat transfer (ratio of heat generation of microwave dielectric heating to thermal diffusion
Atwood number	A	$\mathrm {A} ={\frac {\rho _{1}-\rho _{2}}{\rho _{1}+\rho _{2}}}$	fluid mechanics (onset of instabilities in fluid mixtures due to density differences)
Bagnold number	Ba	$\mathrm {Ba} ={\frac {\rho d^{2}\lambda ^{1/2}{\dot {\gamma }}}{\mu }}$	fluid mechanics, geology (ratio of grain collision stresses to viscous fluid stresses in flow of a granular material such as grain and sand)
Bejan number (fluid mechanics)	Be	$\mathrm {Be} ={\frac {\Delta PL^{2}}{\mu \alpha }}$	fluid mechanics (dimensionless pressure drop along a channel)
Bejan number (thermodynamics)	Be	$\mathrm {Be} ={\frac {{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}}{{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}+{\dot {S}}'_{\mathrm {gen} ,\,\Delta p}}}$	thermodynamics (ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction)
Bingham number	Bm	$\mathrm {Bm} ={\frac {\tau _{y}L}{\mu V}}$	fluid mechanics, rheology (ratio of yield stress to viscous stress)
Biot number	Bi	$\mathrm {Bi} ={\frac {hL_{C}}{k_{b}}}$	heat transfer (surface vs. volume conductivity of solids)
Blake number	Bl or B	$\mathrm {B} ={\frac {u\rho }{\mu (1-\epsilon )D}}$	geology, fluid mechanics, porous media (inertial over viscous forces in fluid flow through porous media)
Bond number	Bo	$\mathrm {Bo} ={\frac {\rho aL^{2}}{\gamma }}$	geology, fluid mechanics, porous media (buoyant versus capillary forces, similar to the Eötvös number)
Brinkman number	Br	$\mathrm {Br} ={\frac {\mu U^{2}}{\kappa (T_{w}-T_{0})}}$	heat transfer, fluid mechanics (conduction from a wall to a viscous fluid)
Brownell–Katz number	NBK	$\mathrm {N} _{\mathrm {BK} }={\frac {u\mu }{k_{\mathrm {rw} }\sigma }}$	fluid mechanics (combination of capillary number and Bond number)
Capillary number	Ca	$\mathrm {Ca} ={\frac {\mu V}{\gamma }}$	porous media, fluid mechanics (viscous forces versus surface tension)
Chandrasekhar number	Q	$\mathrm {Q} ={\frac {{B_{0}}^{2}d^{2}}{\mu _{0}\rho \nu \lambda }}$	magnetohydrodynamics (ratio of the Lorentz force to the viscosity in magnetic convection)
Colburn J factors	JM, JH, JD		turbulence; heat, mass, and momentum transfer (dimensionless transfer coefficients)
Darcy friction factor	Cf or fD		fluid mechanics (fraction of pressure losses due to friction in a pipe; four times the Fanning friction factor)
Dean number	D	$\mathrm {D} ={\frac {\rho Vd}{\mu }}\left({\frac {d}{2R}}\right)^{1/2}$	turbulent flow (vortices in curved ducts)
Deborah number	De	$\mathrm {De} ={\frac {t_{\mathrm {c} }}{t_{\mathrm {p} }}}$	rheology (viscoelastic fluids)
Drag coefficient	cd	$c_{\mathrm {d} }={\dfrac {2F_{\mathrm {d} }}{\rho v^{2}A}}\,,$	aeronautics, fluid dynamics (resistance to fluid motion)
Eckert number	Ec	$\mathrm {Ec} ={\frac {V^{2}}{c_{p}\Delta T}}$	convective heat transfer (characterizes dissipation of energy; ratio of kinetic energy to enthalpy)
Ekman number	Ek	$\mathrm {Ek} ={\frac {\nu }{2D^{2}\Omega \sin \varphi }}$	geophysics (viscous versus Coriolis forces)
Eötvös number	Eo	$\mathrm {Eo} ={\frac {\Delta \rho \,g\,L^{2}}{\sigma }}$	fluid mechanics (shape of bubbles or drops)
Ericksen number	Er	$\mathrm {Er} ={\frac {\mu vL}{K}}$	fluid dynamics (liquid crystal flow behavior; viscous over elastic forces)
Euler number	Eu	$\mathrm {Eu} ={\frac {\Delta {}p}{\rho V^{2}}}$	hydrodynamics (stream pressure versus inertia forces)
Excess temperature coefficient	$\Theta _{r}$	$\Theta _{r}={\frac {c_{p}(T-T_{e})}{U_{e}^{2}/2}}$	heat transfer, fluid dynamics (change in internal energy versus kinetic energy)
Fanning friction factor	f		fluid mechanics (fraction of pressure losses due to friction in a pipe; 1/4th the Darcy friction factor)
Fourier number	Fo	$\mathrm {Fo} ={\frac {\alpha t}{L^{2}}}$	heat transfer, mass transfer (ratio of diffusive rate versus storage rate)
Froude number	Fr	$\mathrm {Fr} ={\frac {v}{\sqrt {g\ell }}}$	fluid mechanics (wave and surface behaviour; ratio of a body's inertia to gravitational forces)
Galilei number	Ga	$\mathrm {Ga} ={\frac {g\,L^{3}}{\nu ^{2}}}$	fluid mechanics (gravitational over viscous forces)
Görtler number	G	$\mathrm {G} ={\frac {U_{e}\theta }{\nu }}\left({\frac {\theta }{R}}\right)^{1/2}$	fluid dynamics (boundary layer flow along a concave wall)
Graetz number	Gz	$\mathrm {Gz} ={D_{H} \over L}\mathrm {Re} \,\mathrm {Pr}$	heat transfer, fluid mechanics (laminar flow through a conduit; also used in mass transfer)
Grashof number	Gr	$\mathrm {Gr} _{L}={\frac {g\beta (T_{s}-T_{\infty })L^{3}}{\nu ^{2}}}$	heat transfer, natural convection (ratio of the buoyancy to viscous force)
Hagen number	Hg	$\mathrm {Hg} =-{\frac {1}{\rho }}{\frac {\mathrm {d} p}{\mathrm {d} x}}{\frac {L^{3}}{\nu ^{2}}}$	heat transfer (ratio of the buoyancy to viscous force in forced convection)
Hydraulic gradient	i	$i={\frac {\mathrm {d} h}{\mathrm {d} l}}={\frac {h_{2}-h_{1}}{\mathrm {length} }}$	fluid mechanics, groundwater flow (pressure head over distance)
Karlovitz number	Ka	$\mathrm {Ka} ={\frac {t_{F}}{t_{\eta }}}$	turbulent combustion (characteristic chemical time scale to Kolmogorov time scale)
Keulegan–Carpenter number	KC	$\mathrm {K_{C}} ={\frac {V\,T}{L}}$	fluid dynamics (ratio of drag force to inertia for a bluff object in oscillatory fluid flow)
Knudsen number	Kn	$\mathrm {Kn} ={\frac {\lambda }{L}}$	gas dynamics (ratio of the molecular mean free path length to a representative physical length scale)
Kutateladze number	Ku	$\mathrm {Ku} ={\frac {U_{h}\rho _{g}^{1/2}}{\left({\sigma g(\rho _{l}-\rho _{g})}\right)^{1/4}}}$	fluid mechanics (counter-current two-phase flow)
Laplace number	La	$\mathrm {La} ={\frac {\sigma \rho L}{\mu ^{2}}}$	fluid dynamics (free convection within immiscible fluids; ratio of surface tension to momentum-transport)
Lewis number	Le	$\mathrm {Le} ={\frac {\alpha }{D}}={\frac {\mathrm {Sc} }{\mathrm {Pr} }}$	heat and mass transfer (ratio of thermal to mass diffusivity)
Lift coefficient	CL	$C_{\mathrm {L} }={\frac {L}{q\,S}}$	aerodynamics (lift available from an airfoil at a given angle of attack)
Lockhart–Martinelli parameter	$\chi$	$\chi ={\frac {m_{\ell }}{m_{g}}}{\sqrt {\frac {\rho _{g}}{\rho _{\ell }}}}$	two-phase flow (flow of wet gases; liquid fraction)
Mach number	M or Ma	$\mathrm {M} ={\frac {v}{v_{\mathrm {sound} }}}$	gas dynamics (compressible flow; dimensionless velocity)
Magnetic Reynolds number	Rm	$\mathrm {R} _{\mathrm {m} }={\frac {UL}{\eta }}$	magnetohydrodynamics (ratio of magnetic advection to magnetic diffusion)
Manning roughness coefficient	n		open channel flow (flow driven by gravity)
Marangoni number	Mg	$\mathrm {Mg} =-{\frac {\mathrm {d} \sigma }{\mathrm {d} T}}{\frac {L\Delta T}{\eta \alpha }}$	fluid mechanics (Marangoni flow; thermal surface tension forces over viscous forces)
Markstein number	${\mathcal {M}}$	${\mathcal {M}}={\frac {{\mathcal {L}}_{b}}{\delta _{L}}}$	fluid dynamics, combustion (turbulent combustion flames)
Morton number	Mo	$\mathrm {Mo} ={\frac {g\mu _{c}^{4}\,\Delta \rho }{\rho _{c}^{2}\sigma ^{3}}}$	fluid dynamics (determination of bubble/drop shape)
Nusselt number	Nu	$\mathrm {Nu} _{d}={\frac {hd}{k}}$	heat transfer (forced convection; ratio of convective to conductive heat transfer)
Ohnesorge number	Oh	$\mathrm {Oh} ={\frac {\mu }{\sqrt {\rho \sigma L}}}={\frac {\sqrt {\mathrm {We} }}{\mathrm {Re} }}$	fluid dynamics (atomization of liquids, Marangoni flow)
Péclet number	Pe	$\mathrm {Pe} _{d}={\frac {du\rho c_{p}}{k}}=\mathrm {Re} _{d}\,\mathrm {Pr}$	heat transfer (advection–diffusion problems; total momentum transfer to molecular heat transfer)
Péclet number	Pe	$\mathrm {Pe} _{d}={\frac {du}{D}}=\mathrm {Re} _{d}\,\mathrm {Sc}$	mass transfer (advection–diffusion problems; total momentum transfer to diffusive mass transfer)
Prandtl number	Pr	$\mathrm {Pr} ={\frac {\nu }{\alpha }}={\frac {c_{p}\mu }{k}}$	heat transfer (ratio of viscous diffusion rate over thermal diffusion rate)
Pressure coefficient	CP	$C_{p}={p-p_{\infty } \over {\frac {1}{2}}\rho _{\infty }V_{\infty }^{2}}$	aerodynamics, hydrodynamics (pressure experienced at a point on an airfoil; dimensionless pressure variable)
Rayleigh number	Ra	$\mathrm {Ra} _{x}={\frac {g\beta }{\nu \alpha }}(T_{s}-T_{\infty })x^{3}$	heat transfer (buoyancy versus viscous forces in free convection)
Reynolds number	Re	$\mathrm {Re} _{L}={\frac {vL\rho }{\mu }}$	fluid mechanics (ratio of fluid inertial and viscous forces)
Richardson number	Ri	$\mathrm {Ri} ={\frac {gh}{u^{2}}}={\frac {1}{\mathrm {Fr} ^{2}}}$	fluid dynamics (effect of buoyancy on flow stability; ratio of potential over kinetic energy)
Roshko number	Ro	$\mathrm {Ro} ={fL^{2} \over \nu }=\mathrm {St} \,\mathrm {Re}$	fluid dynamics (oscillating flow, vortex shedding)
Schmidt number	Sc	$\mathrm {Sc} _{D}={\frac {\nu }{D}}$	mass transfer (viscous over molecular diffusion rate)
Shape factor	H	$H={\frac {\delta ^{*}}{\theta }}$	boundary layer flow (ratio of displacement thickness to momentum thickness)
Sherwood number	Sh	$\mathrm {Sh} _{D}={\frac {KL}{D}}$	mass transfer (forced convection; ratio of convective to diffusive mass transport)
Sommerfeld number	S	$\mathrm {S} =\left({\frac {r}{c}}\right)^{2}{\frac {\mu N}{P}}$	hydrodynamic lubrication (boundary lubrication)
Stanton number	St	$\mathrm {St} ={\frac {h}{c_{p}\rho V}}={\frac {\mathrm {Nu} }{\mathrm {Re} \,\mathrm {Pr} }}$	heat transfer and fluid dynamics (forced convection)
Stokes number	Stk or Sk	$\mathrm {Stk} ={\frac {\tau U_{o}}{d_{c}}}$	particles suspensions (ratio of characteristic time of particle to time of flow)
Strouhal number	St or Sr	$\mathrm {St} ={\omega L \over v}$	fluid dynamics (continuous and pulsating flow; nondimensional frequency)
Stuart number	N	$\mathrm {N} ={\frac {B^{2}L_{c}\sigma }{\rho U}}={\frac {\mathrm {Ha} ^{2}}{\mathrm {Re} }}$	magnetohydrodynamics (ratio of electromagnetic to inertial forces)
Taylor number	Ta	$\mathrm {Ta} ={\frac {4\Omega ^{2}R^{4}}{\nu ^{2}}}$	fluid dynamics (rotating fluid flows; inertial forces due to rotation of a fluid versus viscous forces)
Ursell number	U	$\mathrm {U} ={\frac {H\,\lambda ^{2}}{h^{3}}}$	wave mechanics (nonlinearity of surface gravity waves on a shallow fluid layer)
Vadasz number	Va	$\mathrm {Va} ={\frac {\phi \,\mathrm {Pr} }{\mathrm {Da} }}$	porous media (governs the effects of porosity $\phi$, the Prandtl number and the Darcy number on flow in a porous medium)
Wallis parameter	j*	$j^{*}=R\left({\frac {\omega \rho }{\mu }}\right)^{\frac {1}{2}}$	multiphase flows (nondimensional superficial velocity)
Weber number	We	$\mathrm {We} ={\frac {\rho v^{2}l}{\sigma }}$	multiphase flow (strongly curved surfaces; ratio of inertia to surface tension)
Weissenberg number	Wi	$\mathrm {Wi} ={\dot {\gamma }}\lambda$	viscoelastic flows (shear rate times the relaxation time)
Womersley number	$\alpha$	$\alpha =R\left({\frac {\omega \rho }{\mu }}\right)^{\frac {1}{2}}$	biofluid mechanics (continuous and pulsating flows; ratio of pulsatile flow frequency to viscous effects)
Zel'dovich number	$\beta$	$\beta ={\frac {E}{RT_{f}}}{\frac {T_{f}-T_{o}}{T_{f}}}$	fluid dynamics, Combustion (Measure of activation energy)

Solids

Name	Standard symbol	Definition	Field of application
Coefficient of kinetic friction	$\mu _{k}$		mechanics (friction of solid bodies in translational motion)
Coefficient of static friction	$\mu _{s}$		mechanics (friction of solid bodies at rest)
Dieterich-Ruina-Rice number	$\mathrm {R_{u}}$	$\mathrm {R_{u}} ={\frac {W}{L}}{\frac {(b-a){\bar {\sigma }}}{G}}$	mechanics, friction, rheology, geophysics (stiffness ratio for frictional contacts)
Föppl–von Kármán number	$\gamma$	$\gamma ={\frac {Yr^{2}}{\kappa }}$	virology, solid mechanics (thin-shell buckling)
Rockwell scale	–		mechanical hardness (indentation hardness of a material)
Rolling resistance coefficient	Crr	$C_{rr}={\frac {F}{N_{f}}}$	vehicle dynamics (ratio of force needed for motion of a wheel over the normal force)

Optics

Name	Standard symbol	Definition	Field of application
Abbe number	V	$V={\frac {n_{d}-1}{n_{F}-n_{C}}}$	optics (dispersion in optical materials)
f-number	N	$N={\frac {f}{D}}$	optics, photography (ratio of focal length to diameter of aperture)
Fresnel number	F	${\mathit {F}}={\frac {a^{2}}{L\lambda }}$	optics (slit diffraction)
Refractive index	n	$n={\frac {c}{v}}$	electromagnetism, optics (speed of light in vacuum over speed of light in a material)
Transmittance	T	$T={\frac {I}{I_{0}}}$	optics, spectroscopy (the ratio of the intensities of radiation exiting through and incident on a sample)

Mathematics and statistics

Name	Standard symbol	Definition	Field of application
Coefficient of determination	$R^{2}$		statistics (proportion of variance explained by a statistical model)
Coefficient of variation	${\frac {\sigma }{\mu }}$	${\frac {\sigma }{\mu }}$	statistics (ratio of standard deviation to expectation)
Correlation	ρ or r	${\frac {\operatorname {E} [(X-\mu _{X})(Y-\mu _{Y})]}{\sigma _{X}\sigma _{Y}}}$	statistics (measure of linear dependence)
Courant–Friedrich–Levy number	C or 𝜈	$C={\frac {u\,\Delta t}{\Delta x}}$	mathematics (numerical solutions of hyperbolic PDEs)
Euler's number	e	$e=\displaystyle \sum \limits _{n=0}^{\infty }{\dfrac {1}{n!}}\approx 2.71828$	mathematics (base of the natural logarithm)
Feigenbaum constants	$\alpha$, $\delta$	$\alpha \approx 2.50290,$ $\ \delta \approx 4.66920$	chaos theory (period doubling)
Golden ratio	$\varphi$	$\varphi ={\frac {1+{\sqrt {5}}}{2}}\approx 1.61803$	mathematics, aesthetics (long side length of self-similar rectangle)
Pi	$\pi$	$\pi ={\frac {C}{D}}\approx 3.14159$	mathematics (ratio of a circle's circumference to its diameter)
Radian measure	rad	${\text{arc length}}/{\text{radius}}$	mathematics (measurement of planar angles, 1 radian = 180/π degrees)
Steradian measure	sr		measurement of solid angles

Geography, geology and geophysics

Name	Standard symbol	Definition	Field of application
Albedo	$\alpha$	$\alpha =(1-D){\bar {\alpha }}(\theta _{i})+D{\bar {\bar {\alpha }}}$	climatology, astronomy (reflectivity of surfaces or bodies)
Love numbers	h, k, l		geophysics (solidity of earth and other planets)
Porosity	$\phi$	$\phi ={\frac {V_{\mathrm {V} }}{V_{\mathrm {T} }}}$	geology, porous media (void fraction of the medium)
Rossby number	Ro	$\mathrm {Ro} ={\frac {U}{Lf}}$	geophysics (ratio of inertial to Coriolis force)

Sport

Name	Standard symbol	Definition	Field of application
Blondeau number	$B_{\kappa }$	$\mathrm {B_{\kappa }} ={\frac {t_{g}v_{f}}{l_{mf}}}$	sport science, team sports
Gain ratio	–		bicycling (system of representing gearing; length traveled over length pedaled)
Goal difference	GD	${\text{Goal difference}}={\text{goals scored}}-{\text{goals conceded}}$	Association football
Runs Per Wicket Ratio	RpW ratio	${\text{RpW ratio }}={\frac {\text{runs scored}}{\text{wickets lost}}}\div {\frac {\text{runs conceded}}{\text{wickets taken}}}$	cricket
Winning percentage	–	Various, e.g. ${\frac {\text{Games won}}{\text{Games played}}}$ or ${\frac {\text{Points won}}{\text{Points contested}}}$	Various sports

Other fields

Name	Standard symbol	Definition	Field of application
Capacity factor		${\frac {\text{actual electrical energy output}}{\text{maximum possible electrical energy output}}}$	energy
Cohesion number	Coh	$Coh={\frac {1}{\rho g}}\left({\frac {\Gamma ^{5}}{{E^{*}}^{2}{R^{*}}^{8}}}\right)^{\frac {1}{3}}$	Chemical engineering, material science, mechanics (A scale to show the energy needed for detaching two solid particles)
Cost of transport	COT	$\mathrm {COT} ={\frac {E}{mgd}}$	energy efficiency, economics (ratio of energy input to kinetic motion)
Damping ratio	$\zeta$	$\zeta ={\frac {c}{2{\sqrt {km}}}}$	mechanics, electrical engineering (the level of damping in a system)
Darcy number	Da	$\mathrm {Da} ={\frac {K}{d^{2}}}$	porous media (ratio of permeability to cross-sectional area)
Decibel	dB		acoustics, electronics, control theory (ratio of two intensities or powers of a wave)
Dukhin number	Du	$\mathrm {Du} ={\frac {\kappa ^{\sigma }}{{\mathrm {K} _{m}}a}}$	colloid science (ratio of electric surface conductivity to the electric bulk conductivity in heterogeneous systems)
Elasticity (economics)	E	$E_{x,y}={\frac {\partial \ln(x)}{\partial \ln(y)}}={\frac {\partial x}{\partial y}}{\frac {y}{x}}$	economics (response of demand or supply to price changes)
Fine-structure constant	$\alpha$	$\alpha ={\frac {e^{2}}{4\pi \varepsilon _{0}\hbar c}}$	quantum electrodynamics (QED) (coupling constant characterizing the strength of the electromagnetic interaction)
Gain	–		electronics (signal output to signal input)
Havnes parameter	$P_{H}$	$P_{H}={\frac {Z_{d}n_{d}}{n_{i}}}$	In Dusty plasma physics, ratio of the total charge $Z_{d}$ carried by the dust particles $d$ to the charge carried by the ions $i$, with $n$ the number density of particles
Helmholtz number	$He$	$He={\frac {\omega a}{c_{0}}}=k_{0}a$	The most important parameter in duct acoustics. If $\omega$ is the dimensional frequency, then $k_{0}$ is the corresponding free field wavenumber and $He$ is the corresponding dimensionless frequency
Iribarren number	Ir	$\mathrm {Ir} ={\frac {\tan \alpha }{\sqrt {H/L_{0}}}}$	wave mechanics (breaking surface gravity waves on a slope)
Load factor		${\frac {\text{average load}}{\text{peak load}}}$	energy
Lundquist number	S	$S={\frac {\mu _{0}LV_{A}}{\eta }}$	plasma physics (ratio of a resistive time to an Alfvén wave crossing time in a plasma)
Peel number	NP	$N_{\mathrm {P} }={\frac {\text{Restoring force}}{\text{Adhesive force}}}$	coating (adhesion of microstructures with substrate)
Perveance	K	${K}={\frac {I}{I_{0}}}\,{\frac {2}{{\beta }^{3}{\gamma }^{3}}}(1-\gamma ^{2}f_{e})$	charged particle transport (measure of the strength of space charge in a charged particle beam)
Pierce parameter	$C$	$C^{3}={\frac {Z_{c}I_{K}}{4V_{K}}}$	Traveling wave tube
Pixel	px		digital imaging (smallest addressable unit)
Beta (plasma physics)	$\beta$	$\beta ={\frac {nk_{B}T}{B^{2}/2\mu _{0}}}$	Plasma (physics) and Fusion power. Ratio of plasma thermal pressure to magnetic pressure, controlling the level of turbulence in a magnetised plasma.
Poisson's ratio	$\nu$	$\nu =-{\frac {\mathrm {d} \varepsilon _{\mathrm {trans} }}{\mathrm {d} \varepsilon _{\mathrm {axial} }}}$	elasticity (strain in transverse and longitudinal direction)
Power factor	pf	$pf={\frac {P}{S}}$	electrical (real power to apparent power)
Power number	Np	$N_{p}={P \over \rho n^{3}d^{5}}$	fluid mechanics, power consumption by rotary agitators; resistance force versus inertia force)
Prater number	β	$\beta ={\frac {-\Delta H_{r}D_{TA}^{e}C_{AS}}{\lambda ^{e}T_{s}}}$	reaction engineering (ratio of heat evolution to heat conduction within a catalyst pellet)
Q factor	Q	$Q=2\pi f_{r}{\frac {\text{Energy Stored}}{\text{Power Loss}}}$	physics, engineering (Damping ratio of oscillator or resonator; energy stored versus energy lost)
Relative density	RD	$RD={\frac {\rho _{\mathrm {substance} }}{\rho _{\mathrm {reference} }}}$	hydrometers, material comparisons (ratio of density of a material to a reference material—usually water)
Relative permeability	$\mu _{r}$	$\mu _{r}={\frac {\mu }{\mu _{0}}}$	magnetostatics (ratio of the permeability of a specific medium to free space)
Relative permittivity	$\varepsilon _{r}$	$\varepsilon _{r}={\frac {C_{x}}{C_{0}}}$	electrostatics (ratio of capacitance of test capacitor with dielectric material versus vacuum)
Rouse number	P or Z	$\mathrm {P} ={\frac {w_{s}}{\kappa u_{*}}}$	sediment transport (ratio of the sediment fall velocity and the upwards velocity of grain)
Shields parameter	$\tau _{*}$ or $\theta$	$\tau _{\ast }={\frac {\tau }{(\rho _{s}-\rho )gD}}$	sediment transport (threshold of sediment movement due to fluid motion; dimensionless shear stress)
Specific gravity	SG		(same as Relative density)
Stefan number	Ste	$\mathrm {Ste} ={\frac {c_{p}\Delta T}{L}}$	phase change, thermodynamics (ratio of sensible heat to latent heat)
Strain	$\epsilon$	$\epsilon ={\cfrac {\partial {F}}{\partial {X}}}-1$	materials science, elasticity (displacement between particles in the body relative to a reference length)

Bibliography

• "ISO 80000-11:2019 Quantities and units — Part 11: Characteristic numbers". iso.org. Retrieved 2023-08-31.